In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \...In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.展开更多
A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In th...A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound. Also, we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10671019)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20050027007)
文摘In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.
基金the National Nature Science Foundation of China (Grant Nos.10571117,60773078)the Hong Kong Polytechnic University (Grant No.G-YX69) Shuguang Plan of Shanghai Education Development Foundation (Grant No.06SG42)
文摘A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound. Also, we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound.
